Question

To qualify for the finals in a racing event, a race car must achieve an average speed of $250km/h$ on a track with a total length of $2000m$. If a particular car covers the first half of the track at an average speed of $230km/h$, what minimum average speed must it have in the second half of the event to qualify? (in km/h)

• A. $250$
  
• B. $260$
  
• C. $270$
  
• D. $275$
  

Answer 1

The correct option is C $270$

$v_{av}=\frac{L}{t}\to 1$

For the whole track

$v_{av}=250㎞/hr$ and $L=2000m=2㎞$

$\therefore t=\frac{L}{v_{av}}=\frac{2}{250}0.08h$

The car travels first half of the track $\left(1㎞\right)$ with speed $230㎞/hr$. The time of this motion is

$t_1=\frac{1}{230}=0.0043h$

Since the total traveled time should be $0.008h$, then the second part of the track the car should travel

$0.008-0.0043=0.0097h$

Distance of this motion is $1㎞$

$\therefore$ average speed $=v_2=\frac{1}{0.0037}$

$=270㎞/hr$